Hop-limited flooding over dynamic networks M. Vojnović and A. Proutiere Microsoft Research IEEE Infocom 2011, Shanghai, April 2011

Introduction Disseminate a message to all nodes using transmissions between pairs of nodes Dynamic network – Communication link between a pair of nodes alternates between active and inactive state Desired for the dissemination to be time efficient and of low cost Application scenarios: – Mobile networks – Peer-to-peer networks 2

Related work Parsimonious flooding [Baumann et al, PODC 2009] – Message offered by a node only within some fixed time since the message was received by this node k-copy forwarding [Chainterau et al, ToN 2007] – Each node relays the message to at most k other nodes The diameter of opportunistic mobile networks [Chainterau et al, CONEXT 2007] – Characterized expected number of paths between two end nodes within given time for a dynamic network similar to ours (assumed no hop limit constraints) Coupon collector problem – Special case of 1-hop limited flooding 3

k-hop limited flooding Lazy k-hop limited flooding Message can be relayed by a node only if it was first received by this node through at most k hops 4 Message can be relayed by a node only if this node observed a copy of the message transferred through less than k hops

Main questions Q1: What is the completion time of k-hop limited flooding? – Completion time defined as the time for the message to reach given fraction of all nodes Q2: What is the communication cost of k-hop limited flooding? – Communication cost defined as the maximum number of message transmissions per node Q3: How much worse is the lazy version? 5

Assumptions 6

The limit of many nodes k-hop limited flooding: Lazy k-hop limited flooding: fraction of nodes that first received the message through at most i hops by time t * The paper also contains some additional characterizations of the completion time by studying the underlying Markov processes (not in this slide deck) 7 fraction of nodes that observed a copy of the message that was transferred through less than i hops by time t

Performance measures Completion time Communication cost 1 t 8

Special cases (a n = b n = n) 9

Completion time lower bound 10

Completion time 11

Completion time (cont’d) 12

Completion time comparison 13

Communication cost k-hop limited flooding Lazy k-hop limited flooding 14

Communication cost comparison 15

16 Completion time Communication cost k-hop limited flooding Lazy k-hop limited flooding No hop limits

Dissemination delay vs. hops Diminishing improvement with the number of hops 17

Convergence Lazy k = 2 Lazy k = 3 Accurate asymptotes already for small number of nodes 18

Conclusion 19